Database - Matrix question

• davidche

  22 Oct 08, 11:19

  k (B)^ -1  =  4A  +  I

   

  B = ( 2  -1)

         (2    1)

  A = 1/16 * (-1  3)

                    (-6  2)

   

  Find k.

  I is a identity matrix. Btw, what are the special properties of ID matrix that we shld know about? XD

• eagle

  22 Oct 08, 11:46

  First method is to find the inverse of matrix B, and then compare and evaluate for k. It should be a shorter method than my 2nd method, but I'm not sure if inverse matrix is in your syllabus at the moment.

  1st Method:

  k (B)^ -1  =  4A  +  I

  k (1/(2 - (-2)) * (1     1)  =  ( -1/4 + 1     3/4 + 0)
                        (-2    2)         ( -6/4 + 0     2/4 + 1)

  k * (1/4         1/4)   =   (3/4         3/4)
       (-2/4        2/4)       ( -6/4       6/4)

  k * (1/4         1/4)   =   3 *  (1/4         1/4)
       (-2/4        2/4)              ( -2/4       2/4)

  Comparing, k = 3

   

   

   

  2nd Method:

  k (B)^ -1  =  4A  +  I
  k (B)^ -1  =  ( -1/4 + 1     3/4 + 0)
                       ( -6/4 + 0     2/4 + 1)

  k (B)^ -1  = (3/4         3/4)
                      ( -6/4       6/4)

  k (B)^ -1  = 3/4  *  (1         1)
                                 ( -2       2)

  k (B)^ -1 * (B) = 3/4  *  (1         1)    *    (B)
                                         ( -2       2)

  k I = 3/4  *  (1         1)    *    (2     -1)
                     ( -2       2)          (2      1)

  k I = 3/4  *  (1*2 + 1*2         1*-1 + 1*1)
                     (-2*2 + 2*2         -2*-1 + 2*1)

  k I = 3/4  * (4      0)
                    (0       4)

  k I =3 I

  k = 3

• BadzMaro

  22 Oct 08, 11:48

  Eagle so pro..  howd u do it man! How did u maange to find the truth hidden within..!

• Ahm97sic

  22 Oct 08, 17:10

  Hi Davidche and Eagle,

  Dear Davidche, very sorry. I was busy this morning and I had not gone online. Luckily, Eagle saw your question and he has provided you with two approaches to solve the question.

  Dear Eagle, thanks for helping Davidche with the question.

  Dear Davidche and Eagle, please come into my forums (addmaths.sgforums.com and emaths.sgforums.com) more often. OK.

  Regards,

  ahm97sic

  PS : Dear Davidche, I have posted notes and questions for number patterns in the emaths.sgforums.com. Perhaps you will like to take a look of it. Thanks.